Question

solve each inequality. then graph the solution.

1. $4a + 3 > 15$

$4a + 3 - 3 > 15 - 3$
$4a > 12$
$\frac{4a}{4} > \frac{12}{4}$
$a > 3$
(number line graph with open circle at 3, arrow to right)

1. $1 \geq \frac{m}{4} - 3$
2. $5 \geq -\frac{s}{12} - 3$
3. $3x - 2 > -10 + 29$
4. $\frac{n}{9} + 3 + 1 \leq 10 + 2$
5. $8p + 13 + 2p < 103$
6. $5c - 3 - 3\frac{1}{2}c < 12$
7. $5w - 24 + 12 > 20 + 8$
8. $16 - \frac{y}{2} > 15 + 6$
9. $\frac{1}{6}r - 10 - \frac{5}{6}r > 54$
10. $\frac{a}{2} + \frac{a}{3} - 4 > 1$
11. $10 - (-7) < -\frac{k}{2} + 2 + 10$

use with sourcebook lesson 4-7, pages 108-109.
chapter 4

Explanation:

Step1: Solve the inequality \(1 \geq \frac{m}{4} - 3\)

Add 3 to both sides: \(1 + 3 \geq \frac{m}{4} - 3 + 3\)
\(4 \geq \frac{m}{4}\)
Multiply both sides by 4: \(4\times4 \geq \frac{m}{4}\times4\)
\(16 \geq m\) or \(m \leq 16\)

Step2: Graph the solution

On a number line, we draw a closed circle at 16 (since the inequality is "less than or equal to") and shade to the left.

Answer:

The solution to \(1 \geq \frac{m}{4} - 3\) is \(m \leq 16\). The graph has a closed circle at 16 and shading to the left.